# KAOPEN Interaction Sign Flip: Pooled GLS vs Pair Fixed Effects

## Key Finding

| Specification | dZ_1 x kaopen_j | SE | p-value |
|---|---|---|---|
| Pooled GLS (Model 2c) | +0.9670 | 0.3922 | 0.0137 |
| Pair FE + Year FE | +0.1024 | 0.2205 | 0.6423 |
| Between-pair component | +4.7523 | 0.2664 | 0.0000 |
| Within-pair component | -1.3164 | 0.4220 | 0.0018 |

## Variance Decomposition

- **kaopen_j**: 92.4% between-pair, 7.6% within-pair
- **dZ_1_x_kaopen_j**: 93.7% between-pair, 6.3% within-pair
- **dZ_2_x_kaopen_j**: 93.9% between-pair, 6.1% within-pair
- **dZ_3_x_kaopen_j**: 94.0% between-pair, 6.0% within-pair

Pairs with zero within-pair KAOPEN variation: 4,201 / 7,338
Pairs with meaningful variation (SD > 0.5): 1,360

## Interpretation

The sign flip is **not a contradiction** -- it reflects genuinely different estimands:

### Between-pair effect (positive, identified by pooled GLS)
Pairs where the destination country is **permanently more open** (higher mean KAOPEN)
show a **stronger** demographic distance effect on bilateral holdings. This makes economic
sense: capital account openness is a necessary condition for demographically-motivated
capital to flow. Open destinations attract more capital from demographically distant sources.

### Within-pair effect (negative, identified by pair FE)
When a destination country **changes** its KAOPEN (typically by opening up), the
demographic distance effect on bilateral flows **weakens**. This is the opposite of
what a simple "openness facilitates demographic flows" story would predict.

### Why within-pair opening weakens the demographic channel

Several mechanisms could explain why capital account liberalization weakens the
demographic channel:

1. **Composition effect**: Countries that open attract diverse capital inflows --
   carry trade, hot money, speculative flows -- that dilute the demographically-motivated
   component. The demographic signal gets swamped by other motives.

2. **Selection on openers**: Countries that change KAOPEN tend to be
   more open on average (mean KAOPEN = 0.42 vs 0.26 for non-changers).
   These countries may have different demographic-flow dynamics than permanently open countries.

3. **Adjustment dynamics**: When a country first opens, capital flows may initially
   follow gravity/proximity logic rather than demographic fundamentals. The demographic
   channel may take time to establish in newly-opened destinations.

4. **Direction asymmetry**: Among changers, 21 opened while 18 closed.
   If opening attracts non-demographic flows while closing has no effect (ratchet),
   the within-pair estimate captures the dilution from opening.

## Mundlak Decomposition Details

The Mundlak specification adds pair-means of KAOPEN interaction variables to the pooled
regression. This simultaneously estimates between and within effects without absorbing
time-invariant regressors (log_dist, contiguity, etc.).

| Variable | Coef | SE | p-value | Interpretation |
|---|---|---|---|---|
| kaopen_j | +0.1235*** | 0.0276 | 0.0000 | Within-pair effect (conditioned on Mundlak means) |
| dZ_1_x_kaopen_j | -1.3164*** | 0.4220 | 0.0018 | Within-pair effect (conditioned on Mundlak means) |
| dZ_2_x_kaopen_j | +0.1709*** | 0.0574 | 0.0029 | Within-pair effect (conditioned on Mundlak means) |
| dZ_3_x_kaopen_j | -0.0063*** | 0.0022 | 0.0039 | Within-pair effect (conditioned on Mundlak means) |
| kaopen_j_bar | +0.3376*** | 0.0289 | 0.0000 | Between-pair effect |
| dZ_1_x_kaopen_j_bar | +6.0687*** | 0.4637 | 0.0000 | Between-pair effect |
| dZ_2_x_kaopen_j_bar | -0.8322*** | 0.0638 | 0.0000 | Between-pair effect |
| dZ_3_x_kaopen_j_bar | +0.0317*** | 0.0025 | 0.0000 | Between-pair effect |

## KAOPEN Changers

Partners that meaningfully change KAOPEN (within-pair SD > 0.3): 66 / 177

Top changers by within-pair variation:

| Partner | First | Last | Change | SD |
|---|---|---|---|---|
| CPV | -1.254 | 0.077 | +1.331 | 1.498 |
| EGY | 2.029 | -0.175 | -2.204 | 1.287 |
| ISL | 1.022 | 1.526 | +0.504 | 1.277 |
| BGR | 2.281 | 0.446 | -1.834 | 1.218 |
| BIH | -1.254 | -1.254 | +0.000 | 1.212 |
| JAM | 2.281 | 2.029 | -0.252 | 1.115 |
| KOR | -0.175 | 2.281 | +2.456 | 1.009 |
| GEO | 2.281 | 2.281 | +0.000 | 0.932 |
| VEN | -1.939 | -1.939 | +0.000 | 0.916 |
| ARG | -0.860 | -1.254 | -0.394 | 0.909 |

## Conclusion for the Paper

The sign flip between pooled GLS and pair FE is an **informative result**, not a fragility.
It reveals that capital account openness interacts with demographic distance through two
distinct channels:

- **Level effect** (between): Permanently open destinations are where demographic capital goes.
- **Change effect** (within): Opening the capital account does not strengthen (and may weaken)
  the demographic channel, because new openness attracts diverse non-demographic flows.

This is consistent with the broader project finding that KAOPEN **gates** capital flows
(level matters) but the act of opening triggers adjustment dynamics that dilute the
demographic signal.